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1.6     ! takayama    1: % $OpenXM: OpenXM/doc/ascm2001p/design-outline.tex,v 1.5 2001/06/20 05:42:47 takayama Exp $
1.1       noro        2:
1.4       takayama    3: \section{Design Outline and OpenXM Request For Comments}
1.1       noro        4:
1.4       takayama    5: As Schefstr\"om\cite{schefstrom} clarified,
1.1       noro        6: integration of tools and software has three dimensions:
                      7: data, control, and user interface.
                      8:
1.5       takayama    9: Data integration is concerned with the exchange of data between different
1.1       noro       10: software or same software.
                     11: OpenMath \cite{OpenMath} and MP (Multi Protocol) \cite{GKW} are,
                     12: for example, general purpose mathematical data protocols.
                     13: They provide standard ways to express mathematical objects.
1.3       takayama   14: %For example,
                     15: %\begin{verbatim}
                     16: % <OMOBJ>  <OMI> 123 </OMI> </OMOBJ>
                     17: %\end{verbatim}
                     18: %means the (OpenMath) integer $123$ in OpenMath/XML expression.
1.1       noro       19:
1.5       takayama   20: Control integration is concerned with the establishment and management of
1.1       noro       21: inter-software communications.
1.5       takayama   22: Control involves, for example, a way to call subroutines on other processes
1.1       noro       23: and a method to interrupt computations on servers from a client.
                     24: RPC, HTTP, MPI, PVM are regarded as a general purpose control protocols or
                     25: infrastructures.
1.5       takayama   26: MCP (Mathematical Communication Protocol)\cite{iamc}
                     27: and OMEI \cite{omei} are such protocols for mathematics.
1.1       noro       28:
                     29: Although data and control are orthogonal to each other,
1.5       takayama   30: the real world requires both.
1.1       noro       31: NetSolve \cite{netsolve}, OpenMath$+$MCP, MP$+$MCP \cite{iamc},
                     32: and MathLink \cite{mathlink} provide both data and control integration.
1.5       takayama   33: Each integration method has its own features determined by its
1.1       noro       34: own design goals.
                     35: OpenXM (Open message eXchange protocol for Mathematics)
                     36: is a project aiming to integrate data, control and user interfaces
1.3       takayama   37: started by Noro and Takayama.
                     38:
                     39: Noro has been involved in the development of
1.1       noro       40: a computer algebra system Risa/Asir \cite{asir}.
                     41: An interface for interactive distributed computations was introduced
1.3       takayama   42: to Risa/Asir in 1995.
                     43: The model of computation was RPC.
1.1       noro       44: A robust interruption protocol was provided
1.3       takayama   45: by  two communication channels like ftp.
1.1       noro       46: As an application of this protocol,
                     47: a parallel speed-up was achieved for a Gr\"obner basis computation
                     48: to determine all odd order replicable functions
                     49: (Noro and McKay \cite{noro-mckay}).
1.3       takayama   50: Takayama has developed
1.1       noro       51: a special purpose system Kan/sm1 \cite{kan},
1.3       takayama   52: which is a Gr\"obner engine for the ring of differential operators $D$
1.5       takayama   53: and which was designed as a component of larger systems.
1.1       noro       54:
1.5       takayama   55: Noro and Takayama first tried to integrate these existing two
1.3       takayama   56: software systems.
                     57: We believe that an open integrated system is a future of mathematical
1.1       noro       58: software.
1.3       takayama   59: However, we found that it might be just a dream without realizability
                     60: and that it is an important research subject to
                     61: build a prototype of such an integrated system. % Project X
1.6     ! takayama   62: With these experiences, we started the OpenXM project with the following
1.1       noro       63: fundamental architecture, which is currently described in
1.5       takayama   64: the OpenXM-RFC 100  proposed standard %% ``draft standard'' and ``standard''
1.3       takayama   65: \cite{ox-rfc-100}.
1.1       noro       66: \begin{enumerate}
                     67: \item Communication is an exchange of messages. The messages are classified into
                     68: three types:
                     69: DATA, COMMAND, and SPECIAL.
                     70: They are called OX (OpenXM) messages.
                     71: Among the three types,
                     72: {\it OX data messages} wrap mathematical data.
                     73: We use standards of mathematical data formats such as OpenMath and MP
                     74: as well as our own data format {\it CMO}
                     75: ({\it Common Mathematical Object format}),
                     76: which can be expressed in terms of XML.
                     77: \item Servers, which provide services to other processes, are stack machines.
                     78: The stack machine is called the
                     79: {\it OX stack machine}.
                     80: Existing mathematical software systems are wrapped with this stack machine.
                     81: Minimal requirements for a target software wrapped with the OX stack machine
                     82: are as follows:
1.4       takayama   83: (a) The target must have a serialized interface such as a character based
1.1       noro       84: interface.
1.4       takayama   85: (b) An output of the target must be understandable for computer programs;
1.1       noro       86: it should follow a grammar that can be parsed with other software.
                     87: \item Any server may have a hybrid interface;
                     88: it may accept and execute not only stack machine commands,
                     89: but also its original command sequences.
                     90: For example,
                     91: if we send the following string to the {\tt ox\_asir} server
1.4       takayama   92: (OpenXM server of Risa/Asir)
                     93: \verb+" fctr(x^100-y^100); "+
                     94: and call the stack machine command
                     95: \verb+SM_executeStringByLocalParser+
                     96: then the server executes the asir command
1.1       noro       97: \verb+ fctr(x^100-y^100); +
                     98: (factorize $x^{100}-y^{100}$ over ${\bf Q}$)
                     99: and pushes the result onto the stack.
                    100: \end{enumerate}
                    101: OpenXM package  implements the OpenXM-RFC 100 \cite{ox-rfc-100}
                    102: and 101 \cite{ox-rfc-101} based on
                    103: the above fundamental architecture.
1.5       takayama  104: In this paper, we mainly discuss systems implementing
1.1       noro      105: OpenXM-RFC 100 and 101 on TCP/IP.
1.4       takayama  106: %For example, the following is a command sequence to ask $1+1$ from
                    107: %the Asir client to the {\tt ox\_sm1} server through TCP/IP:
                    108: %\begin{verbatim}
                    109: %  P = sm1_start(); ox_push_cmo(P,1); ox_push_cmo(P,1);
                    110: %  ox_execute_string(P,"add"); ox_pop_cmo(P);
                    111: %\end{verbatim}
                    112: %Here, {\tt ox\_sm1} is an OpenXM server of Kan/sm1.
1.1       noro      113:
                    114: Our project of integrating mathematical software
                    115: systems is taking the ``RFC'' approach, which has been
                    116: used to develop internet protocols.
                    117: The OpenXM on MPI \cite{MPI} is currently running on Risa/Asir
                    118: as we will see in Section \ref{section:homog}.
                    119: We are now preparing the OpenXM-RFC 102 ``Mathematical communication
1.4       takayama  120: on MPI'' (draft protocol).
1.1       noro      121: In the rest of the paper, we abbreviate
                    122: OpenXM-RFC 100 and 101 to OpenXM if no confusion arises.
                    123:
                    124:
                    125:
                    126: